Basic Math Examples

$\sqrt{3 y} \cdot \sqrt{5 y}$

Step 1

Multiply $\sqrt{3 y} \sqrt{5 y}$ .

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Step 1.1

Combine using the product rule for radicals.

$\sqrt{3 y (5 y)}$

Step 1.2

Multiply $5$ by $3$ .

$\sqrt{15 y \cdot y}$

Step 1.3

Raise $y$ to the power of $1$ .

$\sqrt{15 (y^{1} y)}$

Step 1.4

Raise $y$ to the power of $1$ .

$\sqrt{15 (y^{1} y^{1})}$

Step 1.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt{15 y^{1 + 1}}$

Step 1.6

Add $1$ and $1$ .

$\sqrt{15 y^{2}}$

Step 2

Reorder $15$ and $y^{2}$ .

$\sqrt{y^{2} \cdot 15}$

Step 3

Pull terms out from under the radical.

$y \sqrt{15}$